1. Introduction
In thermodynamics systems, the irreversibility in the components of the system produce exergy destruction, and the continuous improvement of the performance of energy conversion systems based on exergy analysis has been a priority among researchers in this field of study [
1], from energy analysis of the thermal systems [
2] and trigeneration systems [
3]. However, from all the information available with these traditional analyses, there is no relevant development on the analysis carried out with this methods to make further improvements to the components of a system [
4], so advanced analyses and economic analysis are proposed to facilitate the thermal and economic improvement of the system.
In recent years, new concepts of exergy, such as endogenous/exogenous and avoidable/ unavoidable exergy destruction, have been employed to obtain relevant information for the identification of irreversibilities and thermodynamic inefficiencies in the systems [
5]. In any thermodynamic system, the exergy destruction in the components can be generated in two ways. The first is due to the irreversibilities of the component under study, which is called endogenous exergy destruction, while the second is due to the irreversibilities of the other components that affect the component under study; this is called exogenous exergy destruction [
6]. Thus, its optimization process will depend on the technical and economic limitations of the system, so there will only be a part of the exergy destruction and avoidable/unavoidable investment costs for each component. By uniting these two concepts, it is possible to identify improvements to the system [
7].
Long et al. [
8] evaluated the importance of the working fluid in the thermal performance of an organic Rankine cycle (ORC) by means of an external and internal exergetic analysis, and an optimization analysis based on a genetic algorithm with exergetic efficiency as an objective function. The results of the exergy analysis showed that the organic working fluid affects the exergetic efficiency of the cycle, with the opposite case in the internal part, where the efficiency did not present changes. The results of the optimization showed that the selection of the working fluid depends, to a greater degree, on the optimal evaporation temperature, which increases the exergetic efficiency of the cycle. Long et al. [
9] performed an exergy analysis to evaluate the impacts of the evaporation pressure and ammonia fraction on the ammonia–water mixture of the system performance Kalina, obtaining that the evaporation pressure plays an important value in the internal and external exergetic efficiency. Additionally, optimal values are obtained from these in their ideal operation, as well as the ammonia fractions increasing the exergetic efficiency depending on the evaporation pressure. However, the exergetic efficiency of the cycle depends on the input temperature of the heat source, evaluating the impact of this parameter on internal and external exergetic efficiency.
Tian et al. [
10] developed a techno-economic analysis of a system consisting of an ORC and an internal combustion engine operating with 235 kW diesel, in order to study the performance of 20 organic fluids. The results showed that the highest energy generated per unit of mass flow and the highest energy efficiency are obtained for refrigerant R-141b and refrigerant R-123, respectively. The study is limited to a single engine operating condition, and a traditional exergetic analysis where the real opportunities for both endogenous and exogenous component savings are not shown.
On the other hand, Zare V. [
11], in order to find savings opportunities, added economic criteria to the thermal performance studies, applied to three configurations of an ORC. However, this application was limited to binary geothermal power plants, where the RORC presented better energy results, while from the economic point of view, the simple ORC was the best option because it is integrated by a smaller amount of equipment, which implies a lower acquisition cost. The results do not consider the evaluation of costs by components but of a global system. In addition, studies from the exergetic point of view have been developed in a traditional way, and thermal-economical studies for waste heat recovery systems of gas generation engines through ORC have not been widely integrated. Thus, the literature reports the results of the modeling developed by Kerme and Orfi [
12], who studied the effect of the temperature of the organic fluid at the entrance of an ORC turbine on the energy and exergy performance, obtaining that the increase of the temperature increases the efficiency while total exergy destruction decreases it.
The combination of traditional and advanced exergetic analysis can provide significant thermodynamic information, such as the source and the amount of exergy destroyed by each component [
13], and how much this destruction can be avoided [
14], as in the case of solar energy collectors with a flat plate and a flat plate with a thin plate, resulting in the exergy destruction in the absorbent plate being greater than the rest of components, but according to the advanced exergetic analysis performed, this exergy destruction is endogenous and unavoidable, which means that the irreversibilities of this component are inherent in its operation mode [
15].
Mohammadi et al. [
16] studied a combination of conventional and advanced exergetic analyses in a supercritical CO
2 recompression cycle to determine the potential for improving the thermal cycle performance, where the overall exergetic efficiency reached 17.13%, the system’s maximum best potential was 106.85 MW, and approximately 35% of exergy destruction could be avoided by focusing on components, such as the heat exchanger, turbine, and main compressor. These investigations can be complemented with the help of the combination of exergetic analysis [
17] and economic analysis to obtain thermo-economic costs based on the irreversibilities of the components [
18].
In addition, comparative studies have been carried out on different configurations of waste heat recovery cycles integrated to gas engines [
18] and applications, such as Petrakopoulou et al. [
19], where the first application of an exergo-economic analysis in a CO
2 capture power plant was evaluated, revealing that the costs associated with exergy and investment analyses are endogenous for most components, where it proposed a suggestion for improving some components, such as the reactor, expander, and compressor. The literature review shows the case of a polygeneration plant operating in a geothermal cascade system coupled to an organic Rankine cycle that produces 40 kWe, where improvement potentials were found in the ORC cycle (10.61 kW) and heat exchanger (2.28 kW), while the exergo-economic analysis revealed an electricity production cost of 7.78
$/h and the advanced exergo-economic analysis suggests that the plant heat exchanger is the component with the greatest opportunity to reduce the exergy destruction of the heat exchanger equipment [
20].
Another application was in a combined steam-organic Rankine cycle to recover waste heat from a gas turbine, where an exergo-economic analysis was performed using three different organic fluids (R124, R152a, and R34a), obtaining that the maximum exergy efficiency and the minimum rate of product costs are 57.62% and 396
$/h, respectively. In addition, the parametric study was complemented with genetic algorithm optimization, where it was obtained that the combined cycle with R152a has the best performance from the thermodynamic and exergo-economic point of view among the fluids analyzed [
21].
Advanced exergetic analyses have focused on the ORC cycle, taking into account the advantage of adapting this cycle to another thermal system for different applications, such as waste heat recovery [
22], thermodynamic optimization [
23], and emergy analysis [
24]. Also, several works have combined these studies to obtain improvement potentials. In applications in turbocharged combustion engines, conventional exergetic analysis gives the evaporator and the expander priority improvement potential while advanced exergy analysis suggests the expander and pump as a priority, and the cycle exergy destruction can be reduced by 36.5% [
25]. For applications of advanced exergo-economic analysis taking into account waste heat recovery in geothermal applications, low-temperature solar applications, and waste heat recovery from engine gases, the exergetic efficiency of the ORC improves by 20%, optimizing the system through advanced exergetic analysis and proposing the expander, evaporator, condenser, and pump as improvement potentials. Different organic fluids have been tested in the ORCs to improve their performance, obtaining that pentane, cyclohexane, iso-butene, iso-pentane, and cyclohexane have the highest avoidable endogenous cost corresponding to the heat sources evaluated. In addition, the avoidable endogenous cost is sensitive to the heat source temperature, and it is possible to reduce the heat source temperature increase from 100 to 150 °C by 28% [
26]. Therefore, it has been identified that advanced exergetic and thermo-economic analysis is one of the alternatives to achieve technically and economically favorable operating conditions, and to achieve its application in real conditions.
In response to the inadequate management of energy resources in industrial processes, there is a need to improve the efficiency of equipment and processes, in addition to reducing the environmental impact. Thus, the energy recovery of the exhaust line of the natural gas generation engines is one of the alternatives to increase the thermal efficiency of these systems [
27]. However, this issue has been approached from different approaches but not articulated with alternative generation systems, which leads to an enormous scientific impact since if it is true that different ORC configurations have been studied, these have not been studied from an advanced exergetic point of view and integrated with thermo-economic modeling in real contexts of operation of stationary high-power natural gas turbocharged engines as a means of heat recovery, in order to obtain technically and economically viable solutions that allow their commercial application [
28].
Thus, the main contribution of this work was to perform an advanced thermo-economic analysis of an organic Rankine cycle for a bottoming natural gas engine, and its respective comparison with the results obtained with conventional exergetic and exergo-economic analyses. The analysis of the irreversibilities of each component is presented, and the possible improvements to the cycle are found using the concepts of endogenous/exogenous and avoidable/unavoidable exergy destruction, combinined with the exergo-economic analysis, thus finding the advance cost rate improvement opportunities for each component based on the irreversibilities of the thermal system.
3. Results and Discussion
In this section, the influence of the engine load on the heat recovery system energy and exergy performance integrated into the natural gas engine was studied, as an alterntive to reduce the global operational cost and increase the thermal efficiency [
43]. The engine power control system adjusts internal engine variables, such as the pressure and temperature of the air-fuel mixture before entering the cylinders, and the recirculation percentage, to provide high efficiency in partial load operation of the gas engine. Some energy indicators were proposed to study the performance of the waste heat recovery system based on ORC, as shown in
Figure 3, while the evaporating pressure was set to 675.8 kPa, and toluene was selected as the working fluid [
33]. For safety restriction, all feasible operating points of the proposed system at different engine loads ensured that toluene evaporates completely at the outlet of the evaporator to prevent corrosion of the liquid in the expander, in addition to a gas temperature at the outlet of the evaporator (state 11) being higher than the acid dew temperature (200 °C) to avoid acidic corrosion of the exhaust [
34].
The results show that the absolute increase in thermal efficiency (
Figure 3b) decreases for toluene and cyclohexane, as does the overall energy conversion efficiency (
Figure 3d) with an increasing engine load, while the net power output (
Figure 3a) presents its maximum value with toluene (89.4 kW—97.9%), cyclohexane (73.2 kW—97.9%), and acetone (53.2 kW—91.81%), respectively. However, in an engine operating interval, acetone presents a slight increase in thermal efficiency, and then decreases, presenting a maximum at an 82.68% engine load.
These results are due to a higher engine load, implying an increase in the exhaust gas flow according to the first and second laws of thermodynamics [
44] while a greater energy loss is presented in the recuperator heat exchanger 1 (HX1) because of the evaporation pressure and thermal oil temperature have been limited. As the engine load increases, there is an increase in the fluid evaporating temperature at the evaporator. Therefore, the power increases, which is the main factor for thermal and exergetic efficiency. However, the isentropic turbine efficiency decreases slightly as a consequence of the increase in the thermal oil temperature, causing a decrease in the energy indicators at high engine loads. Likewise, the tendency to increase the power with the engine load is a consequence of both the increase in the inlet thermal oil temperature to the evaporator, which leads to an increase in the toluene mass flow, and the enthalpy difference between the outlet and the inlet of the pump and turbine, but this is more relevant in the turbine.
In addition, the results obtained from the traditional exergetic and exergo-economic analysis are shown in
Table 2, where the exergy and fraction of exergy destroyed,
, shows that the greatest values are present in the heat exchanger 1 (shell and tube heat exchanger) with 32.54%, the evaporator (28.32%), and the condenser with 27.97%. The component with the highest destroyed exergy value (41.95 kW) is heat exchanger 1, being one of the components with the lowest exergetic efficiency of the cycle, due to the large heat exchanger area required and the high temperature difference. The greater the investment and the cost of exergy destroyed, the greater the influence of the component in the system, therefore, the component with the greatest improvement in cost efficiency of the total plant can be defined. In the case study, the components with the greatest opportunities for improvement in this ratio are the condenser and HX 1. Therefore, these components are the most important from a thermodynamic point of view.
The exergo-economic factor, , is the effective parameter that allows us to compare and evaluate the components that make up the system. A high value for this parameter indicates that for the component under study, acquisition costs predominate over operation and maintenance costs. For example, in the case of the condenser, which is the component with the lowest value of the exergo-economic factor, it can be concluded that expenses are mostly related to operating and maintenance costs compared to acquisition costs.
By means of the advanced exergetic analysis, the exergy destruction can be disaggregated for each one of the components. In this way, the real possibilities of improvement can be determined both through the operational and design point of view of the component, and the global consideration of the thermal system. From the solution of Equations (12)–(18), and the unavoidable operation conditions described in
Table 1, the disaggregation of the exergy can be found in its endogenous, exogenous, avoidable, and unavoidable part, as well as avoidable and unavoidable endogenous and its avoidable and unavoidable exogenous counterpart. The determination of the avoidable part of the destroyed exergy is a significant step because it allows identification of opportunities for improvement in the component and its interaction with the rest of the components. Also, this result allows knowledge of which is the optimal way to increase the thermal efficiency of the system, besides providing valuable information about how the components operate together as a global system.
Figure 4 presents a graphical version of the improvement opportunities in each component from the exergetic point.
The results of the advanced exergetic analysis and economic exergetic analysis are presented in
Table 3, where the disaggregation of the destroyed exergy was calculated as a function of the endogenous, exogenous, avoidable, and unavoidable for each of the components under study. The results show that most of the destroyed exergy is endogenous (78.53% of the total destroyed exergy), emphasizing that the interaction between components does not have a significant effect on the overall exergetic performance of the cycle. Similarly, it is noted that the component with the greatest avoidable exergy destroyed in the system is the turbine, with a value of 11.075 kW, where 69.625% is endogenous and 30.374 is exogenous, which means that in the turbine, there is a real great opportunity for improvement. On the other hand, in the unavoidable part, the components with the greatest technological limitations are the HX 1 and evaporator, representing 96.1% of the total unavoidable exergy of the cycle.
The equations presented in
Section 2.5.2 and
Section 2.5.3 were used to calculate the advance exergy destruction costs as shown in
Table 4, which is based on the result of the advanced destroyed exergy.
It can be observed that the endogenous exergy destruction is higher than the exogenous cost in the components of the thermal cycle, which is a consequence of the high endogenous investment costs values for all components of the system with respect to the exogenous investment cost, as shown in
Table 5. Therefore, it can be established that the interaction between components in terms of investment costs is not very relevant in the system; however, for the component under study, it is a parameter of vital importance. Also, it can be observed that the rates of unavoidable investment costs for the components studied showed an inclination in the unavoidable part.
Negative values of exogenous investment cost rates (ZEX, ZAV,EX, ZUN,EX) revealed that investment costs within these components might decrease if investment costs within the other components are increased.
In order to show a comparison of the destroyed exergy relationship between traditional and advanced exergetic analysis,
Figure 5 is shown. In
Figure 5A, a slight difference of the parameter under study is denoted because the one that was calculated by means of the advanced exergetic analysis only emphasizes the exergy that is destroyed by each component, that is to say, the endogenous part (without the interaction that this one has with its surroundings).
However, the relationship of exergy destroyed by the component was also calculated by emphasizing which fraction is borne by the component itself or by the interaction of the component with its surroundings, as shown in
Figure 5B. From this graph, what has been mentioned before is supported, that is, that the interaction between each of the components of the system is not significant in comparison to the exergy that destroys the component under its own operating conditions. A comparative analysis was performed by implementing a new exergo-economic factor calculated by advanced exergetic analysis, as shown in
Figure 6.
As a percentage, it can be seen that the exergo-economic factor, as well as the traditional and advanced approach, presents a similarity in the components that make up the system. So, the main efforts should concentrate on designing the most efficient heat exchangers [
35], with a smaller heat transfer area and less exergy destruction, without increasing the purchase equipment costs.
4. Conclusions
In this paper, the benefit offered by developed traditional and advanced exergetic analysis in thermal systems was shown, in particular in the organic Rankine cycle systems. Exergetic analysis allows determination of the sources of irreversibility in a thermal system, and therefore indicates the starting points of an optimization procedure, and contributes to the rational use of the energetic resources. In the study carried out, it was possible to determine which equipment that resulted in greater destruction of exergy introduced in the waste heat recovery system based on the organic Rankine cycle. The equipment in which the design or operational improvements can be made was also determined, since the implementation of some recommendations is not practical for optimizing the cycle due to operational or design limitations. Therefore, traditional exergy, advanced exergy, and exergo-economic analysis were applied to gain a better understanding of the system performance. Moreover, a comprehensive comparison was conducted to further assess the system from various points of view.
The conventional exergy showed that the heat exchanger 1 had the largest exergy destruction and exergy destruction, and highest investment costs (41.95 kW, 32.54%, and 2.67 USD/h). The results of the energetic and exergetic analysis of the system showed that the exergy destroyed is a measure of the degree of process irreversibility. Thus, in the case of heat exchanger 1, the causes of the irreversibility were due to the heat transfer through a finite temperature difference higher than 100 °C. Similarly, the results of exergy destructions appeared to be in accordance with the exergy efficiencies. That is, a smaller exergy efficiency implies greater exergy destruction in the system components.
Also, the highest exergo-economic factor was found in the pump 2, turbine, and pump 1, with 90.78%, 89.20%, and 85.24%, respectively. These results were a consequence of the high effect of the purchased equipment cost, and the low thermodynamic efficiency in the aforementioned devices, where the probable solution could be the implementation of low-cost components, which are usually characterized by a lower energy efficiency.
Most of the exergy destruction calculated was endogenous (78.53%), emphasizing that the interaction between components does not have a significant effect on the overall exergetic performance of the cycle. The maximum unavoidable exergy was found for the heat exchanger 1, with 90.44%. This indicates that there are not too many ways to improve this component. Nevertheless, other components, such as pump 2, pump 1, and turbine 1, have the minimum unavoidable exergy destruction, with 0.028, 0.03, and 2.819 kW. In addition, the component with the highest cost rate was the condenser with 7.188 USD/h, followed by the heat exchanger 1 with 2.3 USD/h, but the highest avoidable cost rate was found for the turbine with a value of 0.701 USD/h.
On the other hand, the advanced exergo-economic analyses showed that the turbine is the component with the major purchase equipment cost in the system, with a value of 7.898 USD/h, which is 54.09% of the total equipment cost of the system. For all components studied, the endogenous investment cost was higher than the exogenous part, showing the weak relation between them. A comparison was realized between the traditional and advanced exergo-economic factor, which resulted in a similar effect in each component, but the advanced exergy approach presented a slightly higher value, implying that the advanced exergetic analysis gives greater precision in terms of results without ignoring the really great opportunities for improvement.